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DETROIT — Dissident General Motors Corp. shareholder Kirk Kerkorian said Wednesday that he will slash his stake in the troubled automaker by selling 14 million shares of its stock this week.

The sale, announced in a regulatory filing, came on the same day that Kerkorian’s Tracinda Corp. announced plans to offer $55 a share in cash for up to 15 million shares of MGM Mirage Inc. The transaction would boost Kerkorian’s stake in the owner of the Bellagio in Las Vegas and other casinos to more than 60 percent.

In the GM filing with the Securities and Exchange Commission, Tracinda said it had agreed on Monday to sell the shares at $33 each in a private transaction. The agreement will close on Friday, the filing said.

Kerkorian now owns 56 million shares, or 9.9 percent of GM, according to the LionShares.com financial Web site. The sale would reduce his stake to 42 million, or 7.4 percent of the company’s 565.5 million outstanding shares.

Tracinda spokeswoman Carrie Bloom said she could not comment on the GM transaction beyond the SEC filing.

Burnham Securities analyst David Healy said the two transactions may be related, but Kerkorian likely has the resources to buy the MGM stake without selling GM stock.

“He’s giving them the Chinese water drop torture instead of bailing out all at once,” Healy said of the GM sale. “He’s still trying to stir the pot.”